[Advaita-l] Shankara authenticates Shiva as the son of Brahma

[D Gayatri]

//There he is talking about Rudra, an amsha of Lord Shiva. The amshA is
created, not the amshi. That does not mean that he holds Shiva himself to
be a created entity.//

If that is your reading, then so be it. From my perspective, I do not find
evidence to support your reading. Birth of Rudra is mentioned even in Sruti
like Satapatha and Kausitaki brahmanas.